We propose a variable relaxation scheme for the simulation of 1D, two-phase, multicomponent flow in porous media. For these strongly nonlinear systems, traditional high order upwind schemes are impractical: Riemann solutions are not directly available when the phase behavior is complex, and the systems are weakly hyperbolic at isolated points. Relaxation schemes avoid the dependency on the eigenstructure and nonlinear Riemann solvers by approximating the original system with a strongly hyperbolic linear system. We exploit the known information about the eigenvalues to construct first order and second order variable relaxation schemes with much reduced numerical diffusion as compared to the standard relaxation formulations. The proposed second order variable relaxation scheme is competitive in accuracy and efficiency with a third order component-wise ENO reconstruction, and performs at least as well as second order component-wise TVD schemes.
To support decision making, reservoir simulation is used by oil and gas companies to model fluid flow in the reservoir. Because of the complexity of reservoirs, well scenarios, and recovery processes, reservoir management decisions regularly require the use of computationally expensive numerical simulations. Meanwhile, petroleum engineers often deploy fast analytical simulation tools in practice to support decision making when time, budget, or expertise are of concern. Because of the fast speed in model setup and computation of results, the industry is experiencing a growth in the application of analytical reservoir simulation to a wide range of problems. This paper reviews analytical reservoir simulation technology and discusses its business applications to conventional and unconventional resources. The simulation is based on the analytical solution of the diffusion equation in a cuboid homogeneous reservoir, using integral transform method. Isoparametric transformation extends the solution to irregular non-cuboid reservoirs. Regional-scale reservoir heterogeneity is handled by combining solutions on multiple cuboids. The solution is further adapted to complex features such as hydraulic fractures, both planar and fracture network, which are essential for production of unconventional resources. Analytical forward simulation aids the design and optimization of various aspects of well construction. Examples are given in the paper, from interference test design of multilateral well, sensitivity study of tight gas well, to production behavior of shale gas and liquid wells. This paper also shows a simulation case containing multiple shale liquid wells and a quick-look field development planning case involving 64 hydraulically fractured wells honoring flexible drilling schedule. The growing application of "digital oilfield" technology is vastly increasing the amount of data available in real time. The traditional approaches of data assimilation into numerical simulation models often prove impractical from a time and data perspective. However, in combination with screening technology, production data interpretation facilitated by analytical reservoir simulation that includes pressure transient analysis (PTA) and rate transient analysis (RTA) uses the data efficiently and supports decision making for on-time production management. Due to the high speed, analytical reservoir simulation is also used in uncertainty and optimization processes where hundreds of, even thousands of, simulation runs are required. We discuss an example of field development planning (FDP) optimization. The automated workflow accelerates the planning process of well placement in the presence of subsurface uncertainty and operational risks. It allows screening and ranking of field development options in a matter of minutes. With its simplicity, accessibility, and speed, analytical reservoir simulation complements numerical reservoir simulation as a powerful tool supporting E&P decision making.
A novel analytical-numerical hybrid model introduced in SPE 1914441 is used to illustrate through example applications the benefit of having physics-based models that are practical for automation and integration with monitoring and control systems. The solution integrates the reservoir, completion and surface network, resulting in an efficient model that is readily accessible for daily production optimization. It makes a digital twin for every unconventional well affordable by extensive automation and efficient interface enabling management by exception. In this paper, additional example applications complementing those discussed in SPE 191444 are presented. They include optimization of well-hydraulic fractures positioning in multilayer environment and a quantitative discussion of co-linear versus transverse fracture designs and of the benefits of gas lift optimization. The aim is to illustrate the need/utility for a fast, integrated model that can be used to assist in optimizing the completion and that carry over to production enabling daily production optimization that is practical as opposed to solutions that are too onerous to deploy for every well throughout its lifecycle.
Given the pronounced nature of production decline in shale reservoirs, an integrated reservoir-well model that can efficiently anticipate the changes in reservoir and lift parameters over time is required in order to maintain optimum performance. The solution presented in this paper uses a novel integrated reservoir-well model specifically tailored for unconventional reservoirs to calculate the system deliverability and optimize gas injection throughout the well life. The integrated model is deployed in the cloud. It enables automation of the above process and allows more valuable exploitation of oilfied sensors such as multiphase flowmeters and of process control equipment in digital oilfields. The model calculates for each well, the oil rate versus gas injection rate at any time during the well lifecycle by simultaneous solution of the reservoir transient IPR and the wellbore model. The resulting gas demand displays the typical maximum oil production and corresponding maximum gas injection rate beyond which oil rates would decline. The derivative is then used to calculate the gas injection rates versus time that meet a specific predefined economic objective. Single-well and multi-well scenarios are investigated and the impact of gas supply limit is evaluated to illustrate the practical applicability of the solution. Examples illustrate how the gas allocation among the different wells is calculated to achieve the optimum impact. Comparison of the production when gas injection supply is unrestricted versus production results with restricted gas supply is made and results of staggered production are presented.
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